1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# The coefficient of the term independent of x in the expansion of (x+1x2/3âˆ’x1/3+1âˆ’xâˆ’1xâˆ’x1/2)10

A
70
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
B
112
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
C
105
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
D
210
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

## The correct option is D 210Given expression=(x1/3)3+(1)3(x2/3−x1/3+1)−(x−1)x1/2(x1/2−1) =(x1/3+1)+(x2/3−x1/3+1)x2/3−x1/3+1−(x1/2+1)(x1/2−1)x1/2(x1/2−1) =(x1/3+1)−(1+x−1/2)=x1/3−x−1/2 ⇒(x+1x2/3−x1/3+1−x−1x−x1/2)10 =(x+1x2/3−x1/3+1−x−1x−x1/2)10 =(x1/3−x1/2)10 Tr+1in(x1/3−x1/2)10is 10Cr(x1/3)10−r.(−1)r.(x−1/2)r =(−1)r10Crx(10−r3−r2)which is independent of x If (10−r3−r2)=0⇒r=4 Hence required coefficient =10C4(−1)4=210

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Visualising the Coefficients
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program